REGULATING POLE CONVERTERS
or, substituting for E0) and denoting:

435

A
A =

e = A

cos

2n ~

(2n - I)2

cos (2 n - 1) 0

= AI cos #| cos 0 + g cos 3 #^ cos 3 6 + — cos 5 g | cos 5 0

+ jg cos 7§| cos 76 + }..

Thus the third harmonic is a positive maximum for q = 0, or
100 per cent, pole arc, and a negative maximum for q = %, or
33.3 per cent, pole arc.

For maximum direct voltage, q should therefore be made as
small, that is, the pole arc as large, as commutation permits.
In general, the minimum permissible value of q is about 0.15 to
0.20.

The fifth harmonic vanishes for q = 0.20 and q = 0.60, and
the seventh harmonic for q = 0.143, 0.429, and 0.714.

For small values of q, the sum of the fifth and seventh har-
monics is a minimum for about q = 0.18, or 82 per cent, pole arc.
Then for q = 0.18, or 82 per cent, pole arc:

ei = A {0.960 cos 6 + 0.0736 cos 3 6 + 0.0062 cos 5 0

- 0.0081 cos 7 6 + . . .}

= 0.960 A {cos 0 + 0.0766 cos 3 0 + 0.0065 cos 5 0

- 0.0084 cos 7 6 + ... .};

that is, the third harmonic is less than 8 per cent., so that not
much voltage rise can be produced in this manner, while the
fifth and seventh harmonics together are only 1.3 per cent., thus
negligible.

236. Better results are given by reversing or at least lowering
the flux in the center of the field pole. Thus, dividing the pole
face into three equal sections, the middle section, of 27 per cent,
pole arc, gives the voltage curve, q = 0.73, thus:

62 = A {0.411 cos 0 - 0.1062 cos 3 0 + 0.0342 cos 5 0

-0.0035 cos 7 6 . . .}

= 0.411 A {cos 6 - 0.258 cos 3 0 + 0.083 cos 5 0
-0.0085 cos 7 0 . . .}•

The voltage curves given by reducing the pole center to one-

Cil

4 i: